The badge serves as a key to unlock the white holding case holding the gun parts for either Leon's Magnum or Claire's Sub-machine Gun in the Underground Stairs. These are good to grab, as you'll be following up to use the badge in the S.T.A.R.S. Office to get the weapons themselves. But before you combine the badge with the computer tower, examine the badge's backing to reveal a hidden USB. This can then be used to open the armory.
The storage lockers were a “pilot,” the kind of small test that city government frequently uses to test a new or controversial idea. The city offered up the lockers for individuals to use for months-long stretches. At the time, city officials warned that “misuse of the lockers, vandalism, or other unanticipated results,” could force them to cancel the project.